How can I do a “broad” search for flights?

Yes, you can use http://matrix.itasoftware.com - just enter a destination, say LAX, click "Nearby" and pick airports (up to 300mi away I think). However, that's not super interesting as most of those airports are small regional/county airports that don't get mainline carrier service, so you can just enter destination airports (there aren't that many in CA). You can also do this with your departure airport, too.